Some Thoughts About Appealing Directions for the Future of Fuzzy Theory and Technologies Along the Path Traced by Lotfi Zadeh

The quoted text is an interesting instance of a fuzzy object: it is currently known in slightly diversified forms, each rather different from the quoted one, which corresponds to the first known appearance in English of this adage

Grover's algorithm on a Feynman computer

We present an implementation of Grover's algorithm in the framework of Feynman's cursor model of a quantum computer. The cursor degrees of freedom act as a quantum clocking mechanism, and allow Grover's algorithm to be performed using a single, time-independent Hamiltonian. We examine issues of locality and resource usage in implementing such a Hamiltonian. In the familiar language of Heisenberg spin-spin coupling, the clocking mechanism appears as an excitation of a basically linear chain of spins, with occasional controlled jumps that allow for motion on a planar graph: in this sense our model implements the idea of "timing" a quantum algorithm using a continuous-time random walk. In this context we examine some consequences of the entanglement between the states of the input/output register and the states of the quantum clock

Tight Bounds for SVM Classification Error

We find very tight bounds on the accuracy of a Support Vector Machine classification error within the Algorithmic Inference framework. The framework is specially suitable for this kind of classifier since (i) we know the number of support vectors really employed, as an ancillary output of the learning procedure, and (ii) we can appreciate confidence intervals of misclassifying probability exactly in function of the cardinality of these vectors. As a result we obtain confidence intervals that are up to an order narrower than those supplied in the literature, having a slight different meaning due to the different approach they come from, but the same operational function. We numerically check the covering of these intervals

Speed and entropy of an interacting continuous time quantum walk

We present some dynamic and entropic considerations about the evolution of a continuous time quantum walk implementing the clock of an autonomous machine. On a simple model, we study in quite explicit terms the Lindblad evolution of the clocked subsystem, relating the evolution of its entropy to the spreading of the wave packet of the clock. We explore possible ways of reducing the generation of entropy in the clocked subsystem, as it amounts to a deficit in the probability of finding the target state of the computation. We are thus lead to examine the benefits of abandoning some classical prejudice about how a clocking mechanism should operate.Comment: 25 pages, 14 figure

The digital whomanities project. Best practices for digital pedagogy in the pandemic era

This paper aims to enter the ongoing debate about the critical issues of digital pedagogy through the presentation of Digital WHOmanities, a series of online conferences and workshops held at the University of Bologna. Distance learning has become one of the most discussed topics in educational institutions during the spread of Covid-19, revealing a discrepancy between the rapid development of technology and the ability of learning environments to adapt to this turn. In view of this ongoing debate, Digital WHOmanities tried to define the complex and multifaceted figure of the digital humanist and to provide a methodological framework that could foster further online academic initiatives. Specifically, the accurate organization of timing and contents and the adoption of synchronous and asynchronous approaches have highlighted the effectiveness of flexible digital didactics

A systematic review of the literature on the role of tracheostomy in COVID-19 patients

– The Coronavirus Disease 2019 (COVID-19) is a viral infection caused by Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), which emerged in East Asia and spread around the world from December 2019. The most severe stage of COVID-19 pathology is characterized by respiratory distress requiring intubation. In specific cases, tracheostomy is indicated to ensure the safety of the procedure. The aim of our study was to analyze the scientific literature identifying the indications for tracheostomy and safety precautions to reduce contamination. We analyzed the literature from February 2003 to April 2020, including papers on pandemics of other coronaviruses, such As Severe Acute Respiratory Syndrome Coronavirus 1 and Middle East Respiratory Syndrome Coronavirus, to obtain a variety of relevant information. We focused on indications for tracheostomy in patients affected by COVID-19 or related viruses and the measures adopted to perform a safe procedure. We included 35 papers, of which 24 (68.57%) discussed guidelines for tracheostomy indications. All 35 studies discussed the procedures for performing tracheostomy safely. Data obtained indicated that the authors generally agreed on safety measures but expressed different opinions about indications. Therefore, we provided guidelines addressing safety recommendations. After the pandemic has been resolved, we plan to conduct an international retrospective study to identify the criteria for tracheostomy indications

Quantum Annealing and Analog Quantum Computation

We review here the recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations. The concept is introduced in successive steps through the studies of mapping of such computationally hard problems to the classical spin glass problems. The quantum spin glass problems arise with the introduction of quantum fluctuations, and the annealing behavior of the systems as these fluctuations are reduced slowly to zero. This provides a general framework for realizing analog quantum computation.Comment: 22 pages, 7 figs (color online); new References Added. Reviews of Modern Physics (in press

The power of quantum systems on a line

We study the computational strength of quantum particles (each of finite dimensionality) arranged on a line. First, we prove that it is possible to perform universal adiabatic quantum computation using a one-dimensional quantum system (with 9 states per particle). This might have practical implications for experimentalists interested in constructing an adiabatic quantum computer. Building on the same construction, but with some additional technical effort and 12 states per particle, we show that the problem of approximating the ground state energy of a system composed of a line of quantum particles is QMA-complete; QMA is a quantum analogue of NP. This is in striking contrast to the fact that the analogous classical problem, namely, one-dimensional MAX-2-SAT with nearest neighbor constraints, is in P. The proof of the QMA-completeness result requires an additional idea beyond the usual techniques in the area: Not all illegal configurations can be ruled out by local checks, so instead we rule out such illegal configurations because they would, in the future, evolve into a state which can be seen locally to be illegal. Our construction implies (assuming the quantum Church-Turing thesis and that quantum computers cannot efficiently solve QMA-complete problems) that there are one-dimensional systems which take an exponential time to relax to their ground states at any temperature, making them candidates for being one-dimensional spin glasses.Comment: 21 pages. v2 has numerous corrections and clarifications, and most importantly a new author, merged from arXiv:0705.4067. v3 is the published version, with additional clarifications, publisher's version available at http://www.springerlink.co

Quantum Simulations of Classical Annealing Processes

We describe a quantum algorithm that solves combinatorial optimization problems by quantum simulation of a classical simulated annealing process. Our algorithm exploits quantum walks and the quantum Zeno effect induced by evolution randomization. It requires order $1/\sqrt{\delta}$ steps to find an optimal solution with bounded error probability, where $\delta$ is the minimum spectral gap of the stochastic matrices used in the classical annealing process. This is a quadratic improvement over the order $1/\delta$ steps required by the latter.Comment: 4 pages - 1 figure. This work differs from arXiv:0712.1008 in that the quantum Zeno effect is implemented via randomization in the evolutio